def parameter_frame(self, s, mode=Vector([0., 0., 1.])):
basis = []
t = self.parameter_point(s)
orig = t
if (type(mode) == Vector):
vec = mode.unit()
elif mode == 'Xnat':
vec = (1., 0., 0.)
elif mode == 'Ynat':
vec = (0., 1., 0.)
elif mode == 'Znat':
vec = (0., 0., 1.)
tph = self.parameter_point(s + 0.001)
xp = Vector(
[float(tph[0] - t[0]),
float(tph[1] - t[1]),
float(tph[2] - t[2])])
T = xp.unit()
basis.append(T)
B = cross(vec, T)
basis.append(B)
N = cross(T, B)
basis.append(N)
matrix = [None, None, None]
for i in range(3):
matrix[i] = [float(basis[i][j]) for j in range(3)]
return Frame((orig, matrix))
def symmetrize(self, smooth=False, plane_normal=Vector([0., 1., 0.])):
# we will always take the first point of the control polyline as origin of the symmetry plane
new_pol3d = [self.control_polyline[0]]
plane = Plane([self.control_polyline[0], plane_normal.unit()])
for p in self.control_polyline[1:]:
cp = closest_point_on_plane(p, plane)
print 'closest of ' + str(p) + ' is ' + str(cp)
vec = Vector([cp[i] - p[i] for i in range(3)])
new_pol3d.append(Point([cp[i] + vec[i] for i in range(3)]))
return Spline3D(new_pol3d)
def center_arc(pt1, pt2, bulge):
if bulge > 0.:
inc_angle = 4. * np.arctan(bulge)
elif bulge < 0.:
inc_angle = -4. * np.arctan(bulge)
chord = Vector([pt2[i] - pt1[i] for i in range(3)])
mid = Point([0.5 * (pt1[i] + pt2[i]) for i in range(3)])
vec = (chord.norm * 0.5 * bulge * cross(chord, Vector(
(0., 0., 1.))).unit())
summit = Point([mid[i] + vec[i] for i in range(3)])
radius = chord.norm / (2. * np.sin(inc_angle / 2.))
vec = radius * Vector([mid[i] - summit[i] for i in range(3)]).unit()
center = Point([summit[i] + vec[i] for i in range(3)])
return center
def cross(u, v):
pv = []
pv.append(u[1] * v[2] - u[2] * v[1])
pv.append(u[2] * v[0] - u[0] * v[2])
pv.append(u[0] * v[1] - u[1] * v[0])
vp = Vector(pv)
return vp
def extrude_polyline2d(polyline, frame, height):
pol3d = polyline.to_frame(frame)
lines = []
yb_point = Point([frame[0][i] for i in range(3)])
yb_vec = Vector([frame[1][0][i] for i in range(3)]).unit()
print '*************'
print yb_vec
orig = gp_Pnt(frame[0][0], frame[0][1], frame[0][2])
vec = gp_Dir(yb_vec[0], yb_vec[1], yb_vec[2])
plane = gp_Pln(orig, vec)
for i, p in enumerate(pol3d[:-1]):
print p
print 'zob'
gp0 = gp_Pnt(p[0], p[1], p[2])
gp1 = gp_Pnt(pol3d[i + 1][0], pol3d[i + 1][1], pol3d[i + 1][2])
lines.append(BRepBuilderAPI_MakeEdge(gp0, gp1).Edge())
wire = BRepBuilderAPI_MakeWire(lines[0])
for l in lines[1:]:
wire.Add(l)
face = BRepBuilderAPI_MakeFace(wire.Wire())
print 'normal'
print[vec.X(), vec.Y(), vec.Z()]
extrude = BRepPrimAPI_MakePrism(
face.Shape(),
gp_Vec(height * vec.X(), height * vec.Y(), height * vec.Z())).Shape()
return extrude
def intersect_2_segments(seg1, seg2):
from youbastard.geometry.Line import Line
v1 = Vector([seg1[1][i] - seg1[0][i] for i in range(3)])
v2 = Vector([seg2[1][i] - seg2[0][i] for i in range(3)])
l1 = Line([seg1[0], v1])
seg1_parameters = sorted(
[get_parameter(seg1[0], l1),
get_parameter(seg1[1], l1)])
l2 = Line([seg2[0], v2])
seg2_parameters = sorted(
[get_parameter(seg2[0], l2),
get_parameter(seg2[1], l2)])
intersection = intersect_2_lines(l1, l2)
out = False
if intersection and ( seg1_parameters[0] < get_parameter(intersection, l1) < seg1_parameters[1]) and \
( seg2_parameters[0] < get_parameter(intersection, l2) < seg2_parameters[1]):
out = True
return out
def __init__(self, pt1, pt2, thickness, vertical_vector):
super(Wall, self).__init__([pt1, pt2])
vert = vertical_vector.unit()
wall_direction = Vector([pt2[i] - pt1[i] for i in range(3)]).unit()
normal_direction = cross(wall_direction, vertical_vector).unit()
self.matrix = [[normal_direction[i] for i in range(3)],
[vert[i] for i in range(3)],
[wall_direction[i] for i in range(3)]]
self.thickness = thickness
frame = Frame([pt1, self.matrix])
def face_polyline(polyline, frame):
pol3d = polyline.to_frame(frame)
lines = []
yb_point = Point([frame[0][i] for i in range(3)])
yb_vec = Vector([frame[3][i] for i in range(3)]).unit()
orig = gp_Pnt(frame[0][0], frame[0][1], frame[0][2])
vec = gp_Dir(yb_vec[0], yb_vec[1], yb_vec[2])
plane = gp_Pln(orig, vec)
for i, p in enumerate(pol3d[:-1]):
gp0 = gp_Pnt(p[0], p[1], p[2])
gp1 = gp_Pnt(pol3d[i + 1][0], pol3d[i + 1][1], pol3d[i + 1][2])
lines.append(BRepBuilderAPI_MakeEdge(gp0, gp1).Edge())
wire = BRepBuilderAPI_MakeWire(lines[0])
for l in lines[1:]:
wire.Add(l)
face = BRepBuilderAPI_MakeFace(wire.Wire())
return face.Shape()
def parameter_frame(self, s, mode='frenet'):
basis = []
t = interpolate.splev(s, self.tck, der=0)
orig = Point([float(t[i]) for i in range(3)])
if mode == 'frenet':
t = interpolate.splev(s, self.tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
t = interpolate.splev(s, tck, der=2)
xpp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T.unit())
B = cross(xp, xpp)
basis.append(B.unit())
N = cross(B, T)
basis.append(N.unit())
else:
if (type(mode) == Vector):
vec = mode.unit()
elif mode == 'Xnat':
vec = (1., 0., 0.)
elif mode == 'Ynat':
vec = (0., 1., 0.)
elif mode == 'Znat':
vec = (0., 0., 1.)
t = interpolate.splev(s, self.tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T)
B = cross(vec, T)
basis.append(B)
N = cross(T, B)
basis.append(N)
matrix = [None, None, None]
for i in range(3):
matrix[i] = [float(basis[i][j]) for j in range(3)]
return Frame((orig, matrix))
def frame_array(self, mode=Vector([0., 0., 1.]), n=20, mirror=False):
a_frame = []
for i in range(n):
s = float(i) / (float(n - 1))
a_frame.append(self.parameter_frame(s, mode=mode))
return a_frame
ceiling = extrude_polyline2d(horiz, ceiling_frame, 0.5)
polylines = []
all_tree_nodes = []
thick = 0.15
for ipoint, point in enumerate(data['points']):
sector = [point]
for iwall, wall in enumerate(data['walls']):
if ipoint in wall:
nex = None
if wall[0] == ipoint:
nex = data['points'][wall[1]]
elif wall[1] == ipoint:
nex = data['points'][wall[0]]
length = distance(point, nex)
vec = Vector([nex[i] - point[i] for i in range(3)]).unit()
half = Point([point[i] + 0.5 * length * vec[i] for i in range(3)])
sector.append([half, thick])
all_tree_nodes.append(
TreeNode([sector[0]] + [secp[0] for secp in sector[1:]]))
for itreenode, treenode in enumerate(all_tree_nodes):
#thck = all_thicknesses[itreenode]
#treenode.set_thicknesses()
pl = treenode.offset(default_thickness=thick)
polylines.append(pl)
shapes = []
frame = Frame([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])
t = -t
print t
print 'attributes'
print 'cog = ' + str(t.cg)
print 'circumcenter = ' + str(t.circumcenter)
print 'normal = ' + str(t.normal)
print is_on_plane(t.circumcenter, pl)
print is_on_plane(t.cg, pl)
print is_on_plane(Point((0., 0., 0.)), pl)
idtest += 1
pretty_print('TEST n.' + str(idtest) + ': LINES')
p1 = points[0]
v1 = Vector([points[1][i] - points[0][i] for i in range(3)])
l1 = Line((p1, v1))
p2 = points[2]
v2 = Vector([points[1][i] - points[2][i] for i in range(3)])
l2 = Line((p2, v2))
print '======='
print intersect_2_lines(l1, l2)
print '--------------'
print points[1]
print '======='
idtest += 1
pretty_print('TEST n.' + str(idtest) + ': INTERSECT 2 SEGMENTS')
p1 = Point([0., 0., 0.001])
p2 = Point([1., 1., 0.])
p3 = Point([0., 1., 0.])
}
polylines = []
all_tree_nodes = []
thick = 0.2
for ipoint, point in enumerate(data['points']):
sector = [point]
for iwall, wall in enumerate(data['walls']):
if ipoint in wall:
nex = None
if wall[0] == ipoint:
nex = data['points'][wall[1]]
elif wall[1] == ipoint:
nex = data['points'][wall[0]]
length = distance(point, nex)
vec = Vector([nex[i] - point[i] for i in range(3)]).unit()
half = Point([point[i] + 0.5 * length * vec[i] for i in range(3)])
sector.append([half, thick])
all_tree_nodes.append(
TreeNode([sector[0]] + [secp[0] for secp in sector[1:]]))
for itreenode, treenode in enumerate(all_tree_nodes):
#thck = all_thicknesses[itreenode]
#treenode.set_thicknesses()
pl = treenode.offset(default_thickness=0.2)
polylines.append(pl)
import matplotlib.pyplot as plt
for pol in polylines:
plt.plot([p[0] for p in pol], [p[1] for p in pol])
span = 0.8
max_chord = 0.12
scalef = chord_function(0.78)
chordf = lambda s: max_chord * scalef(s)
a_point = [
Point([0., span / float(ndisc), 0.]),
Point([0.01, span / 4, 0.002]),
Point([0., span / 2, 0.01]),
Point([-0.02, 2. * span / 3., 0.015]),
Point([-0.08, span, -0.02])
]
generator = Spline3D(a_point)
fa = generator.frame_array(mode=Vector([0., 0., 1.]), n=ndisc)
#fa = [Frame([[0.,0.,0.], [[0.,0.,1.],[1.,0.,0.],[0.,1.,0.]]])] + fa
shapes = []
generator_extrados = BRepOffsetAPI_ThruSections(False, True)
generator_intrados = BRepOffsetAPI_ThruSections(False, True)
generator_trailing_edge = BRepOffsetAPI_ThruSections(False, True)
generator = BRepOffsetAPI_ThruSections(False, True)
print dir(generator)
chord = lambda x: max_chord * chordf(x)
for i, f in enumerate(fa):
# adimensioned position along span
xspan = distance(fa[0][0], f[0]) / span
def __init__(self,
polyline,
generator,
mode=Vector([0., 0., 1.]),
n=50,
*largs,
**kwargs):
"""
polyline is wether closed 2D polyline
or a dict :
{
'name1' : [opened_polyline 1],
...
'nameN' : [opened_polyline N]
}
the reunion of all these polylines must be closed and have no zero-length segments
generator must be an array of Frames
along the generator, a parameter is designed by a real s in [0., 1.]
in kwargs we define FUNCTIONS for ex :
scale = lambda s: funcscale(s)
rotation = lambda s: funcrotation(s)
translate = lambda s: translate_rotation(s)
...
"""
obj = {}
frame_array = generator.frame_array(mode=mode, n=n)
if (type(polyline) == Polyline2D) and polyline.is_closed:
obj['surface'] = []
print 'closed polyline'
for i, frame in enumerate(frame_array):
s = float(i) / float(n - 1)
if kwargs.has_key('scale'):
scale = kwargs['scale'](s)
else:
scale = 1.
if kwargs.has_key('rotate'):
rotate = kwargs['rotate'](s)
else:
rotate = 0.
if kwargs.has_key('translate'):
translate = kwargs['translate'](s)
else:
translate = [0., 0.]
obj['surface'].append(
polyline.to_frame(frame,
scale=scale,
translate=translate,
rotate=rotate))
elif (type(polyline) == dict):
print 'dico'
for k in polyline.keys():
obj[k] = []
for i, frame in enumerate(frame_array):
s = float(i) / float(n - 1)
if kwargs.has_key('scale'):
scale = kwargs['scale'](s)
else:
scale = 1.
if kwargs.has_key('rotate'):
rotate = kwargs['rotate'](s)
else:
rotate = 0.
if kwargs.has_key('translate'):
translate = kwargs['translate'](s)
else:
translate = [0., 0.]
for k in polyline.keys():
named_polyline = polyline[k]
obj[k].append(
named_polyline.to_frame(frame,
scale=scale,
translate=translate,
rotate=rotate))
super(Extrusion, self).__init__(obj)
def distance(p1, p2):
return Vector([p2[i] - p1[i] for i in range(3)]).norm
def parameter_frame(tck, s, mode='frenet'):
basis = []
t = interpolate.splev(s, tck, der=0)
orig = Point([t[0], t[1], t[2]])
if mode == 'frenet':
t = interpolate.splev(s, tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
t = interpolate.splev(s, tck, der=2)
xpp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T.unit())
B = cross(xp, xpp)
basis.append(B.unit())
N = cross(B, T)
basis.append(N.unit())
if mode == 'Xnat':
t = interpolate.splev(s, tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T)
B = cross((1., 0., 0.), T)
basis.append(B)
N = cross(T, B)
basis.append(N)
if mode == 'Ynat':
t = interpolate.splev(s, tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T)
B = cross((0., 1., 0.), T)
basis.append(B)
N = cross(T, B)
basis.append(N)
if mode == 'Znat':
t = interpolate.splev(s, tck, der=1)
xp = Vector([float(t[0]), float(t[1]), float(t[2])])
T = xp.unit()
basis.append(T)
B = cross((0., 0., 1.), T)
basis.append(B)
N = cross(T, B)
basis.append(N)
matrix = np.zeros((3, 3), dtype=float)
for i in range(3):
matrix[i] = basis[i]
return Frame((orig, matrix))
med_rot = lambda s: 0.
med_gen = ParametricCurve3D(funX, funY, funZ)
medax = Extrusion(cir_pol, med_gen, scale=funR, rotate=med_rot, n=90)
fin_scale = lambda s: 0.08
finR = lambda s: 0.
finX = lambda s: deltaX / 2.
finY = lambda s: 0.
finZ = lambda s: 0.9 * (1. - s)
fin_rot = lambda s: 0.
fin_gen = ParametricCurve3D(finX, finY, finZ)
fin = Extrusion(fin_pol,
fin_gen,
mode=Vector([0., 1., 0.]),
scale=fin_scale,
rotate=fin_rot,
n=13)
print fin
medax.pop_to_geom(geom)
aft_wing.pop_to_geom(geom)
fore_wing.pop_to_geom(geom)
fin.pop_to_geom(geom)
write_geo('medax', geom)
import sys
#fore_cad = extrusion_to_ruled_surfaces(fore_wing, cap = True)
#aft_cad = extrusion_to_ruled_surfaces(aft_wing, cap = True)
wing1 = extrusion_to_solid(fore_wing, 'fore')
x = [0., -0.125, 0.0, .125]
y = [0., 1., 2., 3.]
z = [0., 0.125, 0., -0.125]
pf = Profile(typ='fon', par=[0.99, 0.1, 0.018, 0.035, 0.001],
npt=11) # creation of the 2d profile
pol = pf.polyline(closed=True) # TODO : Profile should herit of Polyline_2D
geom = pg.built_in.Geometry()
a_pt = [Point([x[i], y[i], z[i]]) for i in range(len(x))]
from youbastard.geometry.Spline3D import Spline3D
spline = Spline3D(a_pt)
ndisc = 20
fa = spline.frame_array(mode=Vector([0., 0., 1.]), n=ndisc)
for f in fa:
pp = pol.to_frame(f, scale=0.2)
pp.pop_to_geom(geom)
cpol = spline.control_polyline
pol_gen = spline.discretize(ndisc)
sym = spline.symmetrize()
fasym = sym.frame_array(mode=Vector([0., 0., 1.]), n=ndisc)
sym_pol_gen = sym.discretize(ndisc)
for i, f in enumerate(fa):
bas = f[1]
new_bas = [[-bas[0][0], -bas[0][1], -bas[0][1]],
def piecewise_bezier_polyline(start_value=0., end_value=0., *largs):
import matplotlib.pyplot as plt
from youbastard.geometry.Point import Point
from youbastard.geometry.Vector import Vector
from youbastard.geometry.Line import Line
from youbastard.geo_functions import cross, dot, angle, intersect_2_lines
prev = [0., start_value]
last = [1., end_value]
bezier_parts = [[prev]]
plt.clf()
plt.axis('equal')
plt.scatter([prev[0], last[0]], [prev[1], last[1]], c='k')
for i, cpl in enumerate(largs[0]):
if i == len(largs[0]) - 1:
nex = last
else:
nex = largs[0][i + 1]
pt = [cpl[0], cpl[1]]
tmppt = Point([pt[0], pt[1], 0.])
plt.scatter(pt[0], pt[1], c='k')
rad = cpl[2]
vec1 = Vector([pt[0] - prev[0], pt[1] - prev[1], 0.])
vec2 = Vector([nex[0] - pt[0], nex[1] - pt[1], 0.])
Z = Vector([0., 0., 1.])
ang = angle(vec1, vec2, plane_normal=Z)
if ang > 0.: sgn = 1.
elif ang < 0.: sgn = -1.
print ang
norm1 = sgn * cross(Z, vec1).unit()
norm2 = sgn * cross(Z, vec2).unit()
l1 = Line([Point([prev[0], prev[1], 0.]), vec1])
l2 = Line([Point([pt[0], pt[1], 0.]), vec2])
ln1 = Line([
Point([prev[0] + norm1[0] * rad, prev[1] + norm1[1] * rad, 0.]),
vec1
])
ln2 = Line([
Point([nex[0] + norm2[0] * rad, nex[1] + norm2[1] * rad, 0.]), vec2
])
center_arc = intersect_2_lines(ln1, ln2)
if center_arc:
cen = [center_arc[j] for j in range(2)]
lnorm1 = Line([center_arc, -norm1])
lnorm2 = Line([center_arc, -norm2])
start = intersect_2_lines(lnorm1, l1)
end = intersect_2_lines(lnorm2, l2)
vecstart = Vector([start[i] - tmppt[i] for i in range(3)])
vecend = Vector([end[i] - tmppt[i] for i in range(3)])
if vecstart.norm > 0.5 * vec1.norm:
print 'too long'
tmpvec = vecstart.unit()
start = Point(
[tmppt[i] + 0.5 * vec1.norm * tmpvec[i] for i in range(3)])
if vecend.norm > 0.5 * vec2.norm:
tmpvec = vecend.unit()
end = Point(
[tmppt[i] + 0.5 * vec2.norm * tmpvec[i] for i in range(3)])
bezier_parts[-1].append([start[0], start[1]])
bezier_parts.append([[start[0], start[1]], [pt[0], pt[1]],
[end[0], end[1]]])
bezier_parts.append([[end[0], end[1]]])
plt.scatter([start[0], end[0]], [start[1], end[1]], c='g')
else:
cen = pt
bezier_parts[-1].append([pt[0], pt[1]])
bezier_parts.append([[pt[0], pt[1]]])
plt.scatter(cen[0], cen[1], c='r')
prev = pt
bezier_parts[-1].append([last[0], last[1]])
polx = []
poly = []
for bp in bezier_parts:
polx += [p[0] for p in bp]
poly += [p[1] for p in bp]
plt.plot(polx, poly)
def func(parameter):
ctpts = None
for i, bp in enumerate(bezier_parts):
#print parameter,bp[0][0],bp[-1][0], len(bp)
if (bp[0][0] <= parameter) and (parameter <= bp[-1][0]):
ctpts = bp
break
s = (parameter - ctpts[0][0]) / (ctpts[-1][0] - ctpts[0][0])
return de_casteljau(ctpts, s)[1]
N = 1000
x = [float(i) / float(N - 1) for i in range(N)]
fx = [func(s) for s in x]
plt.plot(x, fx, '.')
plt.show()
return func